### Abstract

Given a finite field F and a linear recurrence relation over F it is possible to find, in a fairly "obvious" way, a finite extension L of F and a subgroup M of the multiplicative group of L such that the elements of M may be written, without repetition, so as to form a cyclically closed sequence which obeys the recurrence. Here we investigate this phenomenon for second-order recurrences; the situation in which F has prime order and the characteristic polynomial of the relation is irreducible over F is described.

Original language | English |
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Pages (from-to) | 413-422 |

Number of pages | 10 |

Journal | Finite Fields And Their Applications |

Volume | 9 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Jan 2003 |

### Keywords

- Finite field
- Group permutation polynomial
- Linear recurrence relation
- Subgroup

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## Cite this

Brison, O. J., & Nogueira, J. E. (2003). Linear recurring sequence subrgroups in finite fields.

*Finite Fields And Their Applications*,*9*(4), 413-422. https://doi.org/10.1016/S1071-5797(03)00014-5